I know it's because of the space taken up by the rear cassette. But why not just make the hub narrower, and not make it asymmetrical? Sure, the drive-side hub flange must be moved inboard to make room for a big cassette. But why not move the other flange inboard as well?

The spokes must be at an angle to provide lateral stiffness to the wheel. However, the wheel must be in static equilibrium, so on a dished wheel with different spoke angles on each side, the drive side and non drive side spokes must be in different tension, or else have different diameter or spoke count. This is well known. But why go to the trouble? Why not move the non drive side flange in as well, and use the same spoke tension on both sides?

Suppose on the drive side, the spoke flange is offset 20mm from the hub centerline, but on the left, the flange is offset 40mm. Obviously, 20mm of offset is sufficient offset for the drive side, in order to impart sufficient strength and stiffness to the wheel. In fact, I postulate that the larger offset of the non drive side is unable to add additional stiffness vs. the 20mm offset of the drive side because the wheel must be in equilibrium. Any additional offset of the non drive side must be compensated for by looser spoke tension, anyway, giving no benefit. So why not just make it 20mm on both sides, and reap the benefits of a shorter, stiffer axle?

It cannot be true that dish provides a laterally or vertically stiffer wheel. The wheel must be in equilibrium, so the stiffness of a dished wheel should be the same as a wheel where both flanges were simply the same distance from centerline as the drive side. In other words, the drive side is the limiting factor. The only advantage I can see to dishing is that the lower spoke tension on the non drive side might allow thinner (but longer!) spokes and thinner hub flange, saving weight. But this seems unlikely to compensate for the weight savings that could be had with a shorter axle.

Another possible reason is an aesthetic desire for a laterally symmetrical frame dropout spacing. But in a world of Lefty forks, is this really a barrier?

I thought of this after seeing a heavy duty touring bike with an un-dished rear wheel.

Not the math, but the physics. Since the wheel is in equilibrium, the spoke forces both laterally and vertically must be the same on both sides of the wheel, regardless of flange geometry. And if we assume the spokes obey Young's law (an extremely good approximation for bicycle spokes) then the stiffness laterally and vertically must also be the same for a dished wheel vs. a symmetric wheel with equal spoke configurations on the drive side. It's not possible for the dish itself to add strength/stiffness because the limiting factor is the weaker side. In fact, dishing causes practical problems.
– BetterSenseFeb 29 at 15:37

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A lot of "must" there. If the rim was laterally very flexible so that parts connected to different spokes would move independently, the argument would make sense. In reality the rim is quite stiff, and all parts get lateral support from the non-drive side. You should note that even though tension on non drive side is much less, the force per lateral displacement depends only on elasticity and angle of the spoke as long as it remains tensioned.
– ojsFeb 29 at 18:43

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Strange how many people misunderstand BetterSense’s question or the physics behind it.
– MichaelMar 2 at 9:53

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The spokes on NDS are tensioned, even if the tension is lower. Because of the lower angle, lateral loads do not have as much effect on tension as on drive side.
– ojsMar 2 at 11:45

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@Michael Because isolating a small section of the rim from the entire system and thinking you can conclude more than a century of bicycle wheel design has all been done wrong is overly simplistic - at best. A sideways force on the rim will induce forces over the entire wheel, and the analysis behind this question completely ignores those forces. The claim here is based on a facile static analysis of a single isolated section of an entire dynamic system. That claim flies in the face of actual design decisions over 100+ years from an entire mature industry.
– Andrew HenleMar 2 at 12:50

4 Answers
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Some rear hubs that have done a version of this include the Ritchey Zero or Z-hubs. The road Zero hub had a 21.3mm center-to-right flange measurement and 28.6 center-to-left, so combined with a 3.65mm or so offset rim it was dishless. (It didn't need an asymmetrical frame, but moving in the left dropout is secondary to whether this sort of idea can work.) These wheels do function and didn't seem to have any grievous reliability problems, so maybe they should have been copied more, but they also don't push the concept all the way to total symmetry.

I believe the deal with this is that there are some physical reasons why if you take the center-to-right flange measurement off a road hub and say, "Okay, if that's strong enough for lateral loads in one direction, then let's make the left one the same," you wind up with a wheel that buckles easily from lateral loads in either direction. In other words it's not just a matter of what bracing angle is good enough per side; in the highly tension-disparate wheels we have, the better bracing angle side is somehow making the whole thing more stable.

I haven't done the deflection tests that would be needed to test whether this is true, but what I have done is build a number of SP generator hubs with their dainty 23.5mm per side center-to-flange dimensions. Those wheels have the unlovely trait that when you do routine side-loading on them to reduce spoke windup, you can feel that they're extremely laterally flexible, and it's easy to induce a "column buckling" type failure if you're not careful, something I have no trouble with in other wheels. People ride them and they work, but from what I've experienced it's clear to me that once you're down to bracing angle numbers like that on each side, the wheel threatens to become too unstable.

Another piece of the puzzle is that, as with so many aspects of bike component design, competitive and sport use is the economic backbone of the industry and so what works there drives what gets made. How it applies here is that existent rear road wheels have been strong enough for competitive use under athletic riders, so doing anything about their lack of strength from being so heavily dished has never been seen as a priority by the mainstream, or worth compromising anything else to fix. Virtually no advantage is ascribed to increasing the strength of the wheel against vertical loads, so why sacrifice any lateral strength to get it, even if it were just in one direction? Were this not the case, offset rims would be ubiquitous, because they work against the problem in a manner that gives up nothing other than some additional costs (and have become common on prefab sets).

When chain-driven bikes were invented, they were single speed, only. The rear triangle was symmetric just as the rear wheels were, as the single sprocket didn't take up much space and could fit easily into the gap between the frame and the spokes.

Then people realized that it would be good to have a number of different gears, and added two more sprockets and a derailleur to the bikes. This was pretty much an after-thought. It did not change the existing parts, it just added parts.

However, as more and more gear were demanded by customers, there was simply not enough space to squeeze the required sprockets in between the frame and an undished rear wheel. So, in order to keep compatibility with existing frames, the rear wheel had to be dished.

That said, there is a second point, the chain-line:

If you were to construct an 11 speed bike with an undished wheel, you'd either end up with a very thin wheel (unstable!) or you'd have to move the right dropout significantly to the right. Your chain rings would need to follow.

This would mean that you either loose space for the crank arms and move the chain dangerously close to the pants, or that you would need to move the pedals outwards. The later would feel quite awkward to most cyclists, and would make cornering much more dangerous (pedal strike).

I'm not saying that you can't do this, but the result would not look and feel like the bikes we ride today.

Wheel dishing and chain line are independent. I am proposing that on 11 speed bikes, to use your example, the gears, chainline, and right dropout position should stay exactly the same. But the left dropout should be moved toward the centerline until the wheel is symmetrical. This would save weight from a shorter axle and frame tubes, without compromising wheel strength, since the drive side flange geometry is the limiting factor of wheel strength anyway. The proposal is a symmetric wheel with an asymmetric rear-end. But riding geometry, chainline and everything the same.
– BetterSenseFeb 29 at 15:32

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@BetterSense The dishing is a compromise to use as much flange spacing as is available, while keeping the chain line and sacrificing only as little flange spacing as possible for the gears. If you want to avoid this compromise, you have two directions to go: In one direction lies a wheel with very little lateral stiffness (your approach), in the other lies a rock-solid wheel (the approach I detailed). To me, the later one is the natural approach as there is no reward in making the wheel even less robust.
– cmaster - reinstate monicaMar 1 at 0:06

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Santana Tandems went to a dishless rear wheel long ago as this provided greater lateral strength to the wheel and thus better endurance/reliability to the wheel. The down side (everything's a compromise) is the chainstays got longer so the stoker's heels wouldn't hit them. And there in lies one of the tradeoffs to the asymmetrical frame: given a road race bike's typical short chainstay length riders with large feet (aka me) would have sever issues with heel impacting the chainstays.
– NoCo RiderMar 1 at 6:11

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@NoCoRider Right, if you use a straight chainstaiy, you run into this problem. However, bikes have been built where the chainstays are not straight, so that's a viable method of avoiding the heel strike problem. That's why I think that the real problem is the chain itself: It needs to be straight, and it should not run at an angle.
– cmaster - reinstate monicaMar 1 at 8:04

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Undished does not mean less heel clearance, but rather more heel clearance on the non drive side. More heel clearance (but asymmetrical clearance) would an advantage not a disadvantage.
– BetterSenseMar 1 at 19:14

I postulate that the larger offset of the non drive side is unable to add additional
stiffness vs. the 20mm offset of the drive side because the wheel must be in equilibrium. Any additional offset of the non drive side must be compensated for by looser spoke tension, anyway, giving no benefit.

This is where your thinking is going wrong. The emphasized sentence in the quote above is false. You are confusing spoke tension with the ability to withstand a lateral force.

Update based on comment:

And the restoring forces in case of deflection are also expected to be the same from both sides, regardless if flange spacing differs

Again, that's false. You are assuming the reaction force in response to a rim deflection is only determined by the balanced lateral force the drive and non-drive side spokes exert on the rim.

What you need to think about is how the forces exerted by the spokes changes as the rim is deflected. The greater the angle the spoke has to the plane of the wheel the more it will elongate for a given rim defection away from it. That means the rate of increase in force as the rim deflects is greater for a larger spoke angle. That's why the non-drive side spoke can exert a higher force in response to rim deflection despite its static tension being lower than the drive side.

The bold sentence is referring to wheel stiffness. It is often stated that the greater non-drive-side flange spacing of a dished wheel is able to create a stiffer wheel. However, there's no way to justify the claim. The horizontal and vertical forces on the rim must be the same from both sides. And the restoring forces in case of deflection are also expected to be the same from both sides, regardless if flange spacing differs. So moving a flange further out, other things being equal, cannot increase wheel stiffness laterally or vertically. Neither can adding more spokes to only one side.
– BetterSenseMar 2 at 18:12

Just do the math. If you assume that spokes obey Hooke's law and the wheel is more or less rigid in vertical direction, you'll find out that force required for lateral displacement depends only on the spring constant and angle of spokes.
– ojsMar 2 at 19:19

Good question. The only reason I can think of is that the average spoke tension of a narrow symmetric rear wheel (i.e. same spoke angle on both sides) would be higher. Wouldn’t this increase the compression force on the cross-section of the rim?

What’s strange is that on classical wheels nobody is really taking advantage of the lower non-drive side forces. In fact, the lower non-drive side spoke tension is a problem because it can lead to spokes loosening over time.

In recent years some asymmetric rear rims have been released which improve the drive side spoke angle a bit (e.g. DT Swiss RR411) and allow for higher non-drive side spoke tension.

Some system wheels take advantage of the lower non-drive side forces by using asymmetric spoke patterns, different spoke counts or different spokes (e.g. carbon spokes on one side only). For example Mavic makes wheels with radial spokes on the drive side and a normal laced pattern on the non-drive side.

In a classical 32 or 36 spoke wheel the average tension is as much compression as the wheel can stand without tacoing. A symmetrical wheel would just have similar tension on both side, which would have its own benefits but not worth the overall weaker wheel.
– ojsMar 2 at 11:42

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""the average spoke tension of a narrow symmetric rear wheel (i.e. same spoke angle on both sides) would be higher. Wouldn’t this increase the compression force on the cross-section of the rim?"" -- This is the best answer that I have got so far. It is something I overlooked and it's accurate. For acceptable lateral stiffness, there is a req'd minimum HORIZONTAL spoke tension. Moving a flange outward doesn't change stiffness, strength, or save weight, but it definitely, legitimately decreases the total radial spoke tension required. in the wheel. I think this is the most correct answer.
– BetterSenseMar 2 at 18:27

Re: 'Moving a flange outward doesn't change stiffness' yes it does. What if the spoke were at a zero degree angle to the plane of the wheel? It wouldn't be able to exert any lateral force at all.
– Argenti ApparatusMar 2 at 19:53

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I should have said "other factors remaining equal, moving a single flange outward doesn't change stiffness in reasonable configurations". Your example proves it. If one flange is at 0mm offset, and the other flange is at 30mm of offset, the spokes on the 30mm offset flange would have to be totally loose for the other flange to be at 0mm--regardless of tension of the spokes on the 0mm flange. The offset spokes would not be exerting any lateral force at all, despite being drastically further offset than the other side. Illustrating that it's the closer flange that determines the stiffness.
– BetterSenseMar 2 at 20:33